Weather has no bearing on shiny rates in Pokemon GO.
The easiest way to find a shiny is to wait for Community Days, when rates hit 1 in 25. Though there are events where the odds are higher, they're less frequent. Additionally, Pokemon from 5-star Raid Battles (e.g. legendaries and Ultra Beasts) have a 1 in 20 chance of being shiny, though they're naturally much more difficult to catch.
Weather (Bulbapedia)
Shiny Pokemon (Bulbapedia)